I've read that one reason that the nobility attending royal court in the 17th century had a passion for wigs, powdered faces, and gloves was the then prevalence of syphilis. By this reasoning those were partly devices to hide the bodily signs of the disease (before bedtime, that is).

A quick Google search turns up lots of so-so evidence to support this explanation, but I am wondering:

Are there any primary sources?

For example, in the form of contemporary or modern medical textbooks that add further (perhaps definite) evidence one way or the other.

Also, do we know what size the epidemic grew to in Europe and how it affected different strata of societies?

I had a go at answering this question but the primary source requirement dovetails into a spiral of low-res scans of 200+ page 16th century proto-medical treatises, using some sadist font-setter's idea of a typeface. Without primary sources I can still confidently say that there is a very strong correlation between the syphilis epidemic of the 16th century and the conveniently perfumed, powered and bushy wigs. The "king was bald" claim doesn't fly since male-pattern baldness existed well before the 16th century.
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LateralFractalOct 23 '13 at 4:58

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A good non-primary source is this article‌​. The best primary source that'll likely map syphilis to wigs is William Clowes' collection of pamphlets as from what I could stomach reading (the horrifying typeface, not the syphilis) the surgeon did detail the dress and social class of his patients.
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LateralFractalOct 23 '13 at 5:07

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"Men and women that have gone under the South pole, must lay off their
furde night-caps in spight of their teeth, and become yeomen of the
vineger bottle: a close periwig hides al the sinnes of an olde
whore-master, but Cucullus non facit Monachum--'tis not their newe
bonnets will keepe them from the old boan-ach."

"Gone under the South Pole" is, as you might guess, a euphemism for fornication. "Lay off their furde (furred) night-caps" seems to refer to loss of hair, and the "vinegar bottle" was a supposed cure for syphilis. (See also p. 19 here.) "A close periwig hides all the sins of an old whore-master" seems to be a relatively straightforward reference to wearing a wig to hide the symptoms of the disease.

"Cucullus non facit Monachum": the hood does not make the monk. In other words, that wig might hide your symptoms but it doesn't change anything.